My wife and I share an ipad 2, ios7. We have separate PCs. Can we have separate Apple IDs and connect the ipad to each computer under the individual ids? Example, I connect and back up etc under my Apple ID, then later she connects, backs up, purchases etc to her computer using her Apple id.
The short answer is no.
While all major desktop operating systems allow users to have multiple logins where their information is sandboxed, iOS doesn't have this concept.
It might make sense for this to be added, but I expected it years ago and it has still not arrived in the mobile market. With phones this doesn't make much sense, but with iPads it does. I've heard of people sharing iPads fairly often, but never phones.